PvP is to test your skills against other people.
Team games really tests how well your team works together. In one random team game i was in today 8/8 of my deaths were because of friendly fire. FFA is more about how well you can dodge all those semi-randomly placed bombs everyone are placing down.
A 1v1 arena would test how good you are not only at dodging bombs but also placing down bombs. It would also be a good way to handle the people that go around calling other people noobs.
http://www.youtube.com/watch?v=wPkHi5xjLLY